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The research provides an effective method for solving dropping shock problems of the nonlinear packaging systems.
Thus, an acoustic fluid model may be non-conservative for strong shock problems.
A two-dimensional (2D) visual computer code to solve the steady state (SS) or transient shock problems including partially ionizing plasma is presented.
Here we solve again the classical Euler equations of compressible gas dynamics on a rectangular domain for the Leblanc problem and on a circular domain in the case of the shock problems of Sedov and Noh.
The tests include the different well-known shock problems described for example by Mignone et al. ([2007]) in regard to the testing of the PLUTO code as well as the magnetic rotor tests described by Romanova et al. ([2009]).
For steady shock problems, the new flux predicts a slightly more diffused profile whereas for unsteady cases, the captured shock is very similar to those produced by the Roe- flux.
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The numerical method is benchmarked for accuracy and tested using two-fluid one-dimensional soliton problem and electromagnetic shock problem.
Two cases, a slowly moving shock problem and a blunt body calculation, are discussed in this paper.
Numerical applications of RBC schemes of order 3, 5 and 7 to a diagonal wave advection and to a converging cylindrical shock problem confirm the theoretical results.
The effectiveness of the method for both fixed and moving grids is demonstrated via several 1D test problems including a standard shock tube problem and an infinite strength reflected shock problem.
For the dropping shock problem of the un-damped cubic-quintic nonlinear packaging system, the correction method of analytical solutions is the same as the above example.
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